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Answer:
W(x) = 27/256(x)(32-x)
Step-by-step explanation:
There are several ways you can do this. The method we've used here is to write a function that has zeros at x=0 and x=32, opens downward, and has a maximum at x=16 of 27.
The zeros give rise to the factored form ...
w = x(x -32)
To make it open downward, we need to reflect this across the x-axis. We can add a leading minus sign, or we can swap the terms in the binomial that has a minus sign:
w = -x(x -32) = x(32 -x)
This will have a value of 16(32 -16) = 256 at its peak. We want the peak to be 27, so we can vertically scale this function by a factor of 27/256. The grap attached shows this gives the desired result.
W(x) = (27/256)(x)(32-x)
